5. A monopolist's profit is given by

=aqbq^2cqtq, where a, b, and c are constants and t is a per unit production tax.

a. Derive an expression for profit maximizing output and then derive an expression for how optimal output changes with the tax

dq/dtfrom this explicit function.

b. Using the implicit function rule, derivedq/dtfrom the first order condition for profit maximization.